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A Pattern In The Lusternik-Schnirelmann Category Of Rational Spaces, Julie Dare Houck
A Pattern In The Lusternik-Schnirelmann Category Of Rational Spaces, Julie Dare Houck
Dissertations
The Lusternik-Schnirelmann (or LS) category of a space is one less than the number of contractible open sets with which we can cover the space. If we look at the LS categories of the skeleta of a CW complex, we find a sequence of dimensions where the LS category changes. I discuss whether certain of these "category sequences" (defined in the paper, "Categorical Sequences", by Nendorf, Scoville, and Strom) could be realized as the categorical sequences of rational spaces. I first reduce from looking at all rational spaces to only Postnikov sections of finite wedges of spheres. Using the Leray-Serre …
"Integration Of Math And Music In The Secondary Classroom", Brian O'Neill
"Integration Of Math And Music In The Secondary Classroom", Brian O'Neill
Honors Theses
The disciplines of mathematics and music seem worlds apart at first glance. Harmonious connections can inevitably be created if a deeper appreciation is lent to these stereotypically dissimilar subjects. "Integration of Mathematics and Music in the Secondary Classroom" is a quadratic function unit that utilizes music to aid in teaching mathematical concepts. The unit consists of a compilation of traditional rote mathematics and three main inquiry lessons: Problems Without Polyrhythm, Ma-Thematics, and The Undertones of Overtones. The unique approach of inquiry allows students to construct meaningful learning through a curriculum that is driven by their own mathematical questions. In addition, …
Weighted Shifts Of Finite Multiplicity, Daniel S. Sievewright
Weighted Shifts Of Finite Multiplicity, Daniel S. Sievewright
Dissertations
We will discuss the structure of weighted shift operators on a separable, infinite dimensional, complex Hilbert space. A weighted shift is said to have multiplicity n when all the weights are n x n matrices. To study these weighted shifts, we will investigate which operators can belong to the Deddens algebras and spectral radius algebras, which can be quite large. This will lead to the necessary and sufficient conditions for these algebras to have a nontrivial invariant subspace.